I have a 2008 Mercury Grand Marquis with 80,000 miles, and the temperature sometimes rises past the middle towards the H. I’ve replaced the thermostat, the fan relay, and the coolant temperature sensor. Last night, while idling in a gas station parking lot, it started overheating, but I shut it off before it did, went to start it again after a few minutes, and it ran fine the rest of the night. Could it be the fan? Thanks!
So you've determined that the fan isn't spinning but it works when it's connected straight to Power.
Check fuse 102 (50Amp) in the engine compartment fuse box.
If it's good then grab a test light and disconnect the fan wiring connector.
Using the test light check for Power on the red wire and Ground on the black wire as the engine exceeds operating temperature.
Here's how it's wired up.

Hook up a scanner and observe the ECT sensor data to make sure that there isn't a wiring problem in the ECT (engine coolant temperature) sensor circuit.
You can also check to see if you're getting Power from fuse 102 (Always) at the fan control module on Pin 1 (Red and Black wire).
If you have Power there, and the ECT sensor temperature looks good on the scanner, and the fan works when connected straight to Power, yet you are lacking either Power or Ground at the Cooling Fan wiring connector as the engine exceeds operating temperature then you'd suspect a faulty fan control module
Could it be the fan?
Why not check it and see?
It kicks on when connected straight to power, but I have no idea if it runs on its own.
Keep an eye on the fan as the car warms up, being careful not to let the engine overheat.
Can confirm, the fan does not go on its own. Took a bit of a detour from work, and when I got home, checked under the hood and the fan blades weren’t moving at all. Any thoughts?
Trace out the circuit fault. Temperature sensor is a prime suspect.
Late response, been out of state, but if you mean the coolant temperature sensor, I’ve already replaced that, my man.
Are your fans working adequately? Even though it's able to kick on doesn't necessarily means it's doing it's job. Upon startup, these panther cars typically have their fan at the radiator roar loud/spin fast & also when the car's overheating. Is it roaring and spinning fast?
Have you checked between the radiator and AC condenser for road debris built up? Partial blockage could cause overheating. (Especially at idle)
Note: It's best to stick with OEM parts as replacements, some aftermarket parts can be iffy.
Some fellas on the LTC Forum mentioned that after you replace the thermostat, the air needs to be bled out of the system to allow it to operate normally. Air trapped in the system could prevent the thermostat from opening/closing properly
Also, check for coolant leaks. These repetitive remarks could lead up to the costly, and common failure, intake manifold replacement. (Pray it's not this, but eventually it'll need to be replaced as your vehicle is 15+ years old)
Good luck!
I happen to recall, this
"https://youtu.be/0DX0FvDm3UA"
would help against air-locks.
(not my video)
@freshoiled2 interesting video, improved burp hole for thermostats..